Virtual Laboratory | Satellite Communication Engineering
Upon completion of this virtual laboratory, students will be able to:
Fundamental principles governing satellite orbital motion and their application to communication satellite systems.
Orbital mechanics (or astrodynamics) is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. For satellite communication engineers, understanding orbital mechanics is essential because the position, velocity, and visibility of a communication satellite directly determine link quality, coverage, and system design parameters.
A satellite in orbit around Earth is in a state of continuous free fall toward Earth, but its tangential velocity is sufficient that it continuously "misses" the Earth, resulting in a closed elliptical path. The motion is governed primarily by Earth's gravitational field, with perturbations from the Moon, Sun, atmospheric drag, and Earth's oblateness.
"The orbit of every satellite is an ellipse with the Earth at one of the two foci."
For artificial satellites, this means that unless the orbit is perfectly circular (a special case of an ellipse where both foci coincide), the satellite's distance from Earth's center varies between a minimum (perigee) and maximum (apogee).
Figure 1: Elliptical orbit geometry showing Earth at one focus, with perigee and apogee distances.
"A line joining a satellite and the Earth sweeps out equal areas during equal intervals of time."
This law is a consequence of the conservation of angular momentum. As a satellite moves from perigee toward apogee, it slows down; as it moves from apogee toward perigee, it speeds up. The velocity is maximum at perigee and minimum at apogee.
Figure 2: Kepler's Second Law — Equal areas swept in equal times. Satellite moves faster near perigee, slower near apogee.
"The square of the orbital period of a satellite is directly proportional to the cube of the semi-major axis of its orbit."
This law allows engineers to determine the orbital period from the orbit size, or conversely, to design an orbit with a specific period. For geostationary satellites, this law precisely determines the required altitude for a 24-hour period.
The velocity of a satellite at any point in its orbit can be determined from the vis-viva equation:
| Orbit Type | Altitude Range | Period | Key Applications |
|---|---|---|---|
| LEO (Low Earth Orbit) | 200 – 2,000 km | ~90 min – 2 hrs | Iridium, Starlink, ISS, remote sensing |
| MEO (Medium Earth Orbit) | 2,000 – 35,786 km | 2 – 12 hrs | GPS, Galileo, GLONASS, O3b |
| GEO (Geostationary) | 35,786 km | 23h 56m 4s | Intelsat, DTH broadcast, weather |
| HEO (Highly Elliptical) | Perigee ~500 km, Apogee ~40,000 km | ~12 – 24 hrs | Molniya, Tundra (high-latitude coverage) |
The coverage area (footprint) of a satellite depends on its orbital altitude and the minimum elevation angle required for communication. Using spherical geometry:
Figure 3: Satellite coverage geometry — coverage area is centered around the subsatellite point (SSP), the point on Earth's surface directly below the satellite.
A ground track is the path traced on Earth's surface directly below a satellite. For non-geostationary orbits, the ground track is determined by:
For a circular orbit, the ground track forms a sinusoidal pattern when projected on a 2D map. The maximum latitude equals the orbital inclination for direct orbits, or 180° - i for retrograde orbits.
Follow these steps to complete the virtual laboratory experiments.
Carefully review the theory section covering Kepler's three laws, orbital parameters, and coverage geometry. Ensure you understand the key equations: vis-viva equation, Kepler's Third Law, and coverage angle formula. Take note of the standard values: Earth's radius Rₑ = 6,371 km, gravitational parameter μ = 3.986 × 10¹⁴ m³/s².
Navigate to Simulation 1. Set the semi-major axis to 8,000 km and eccentricity to 0.3. Observe the elliptical orbit and verify that Earth is at one focus. Run the animation and confirm that the satellite moves faster near perigee and slower near apogee. Record the velocity at perigee and apogee. Verify that equal areas are swept in equal times by measuring the area swept in two different 1-hour intervals.
Use the calculator to determine orbital parameters for the following scenarios: (a) LEO satellite at 800 km altitude with e = 0.001, (b) MEO satellite at 20,200 km altitude (GPS) with e = 0.02, (c) GEO satellite at 35,786 km with e = 0.0001. Record the orbital period, velocity at perigee/apogee, and specific mechanical energy for each case.
Compare GEO, MEO, LEO, and HEO orbits side-by-side. Observe the differences in orbital period, ground track patterns, and Earth coverage. For the HEO orbit, set perigee = 500 km and apogee = 40,000 km. Note how the satellite "hovers" near apogee, making it useful for high-latitude communications. Record your observations on coverage characteristics.
Set an Earth station location (latitude, longitude) and satellite orbital parameters. Run the simulation to determine visibility windows — the time periods when the satellite is above the minimum elevation angle. Vary the orbital inclination and observe how ground track patterns change. For a LEO satellite at 45° inclination, calculate the maximum contact duration per pass and the number of passes per day.
Input various orbital altitudes (from 200 km to 45,000 km) and minimum elevation angles (5°, 10°, 20°, 30°). Calculate and plot the coverage half-angle θ and coverage area for each combination. Determine the minimum number of satellites required for continuous global coverage at each altitude. Compare your results with known constellation designs (Iridium: 66 satellites at 780 km; GPS: 24 satellites at 20,200 km).
Compile all simulation results into organized tables. Plot graphs of: (a) Orbital period vs. altitude, (b) Orbital velocity vs. altitude, (c) Coverage area vs. altitude for different elevation angles, (d) Number of satellites for global coverage vs. altitude. Perform error analysis by comparing simulation results with theoretical calculations.
Follow the report writing guidelines provided in the next section. Ensure all objectives are addressed, all data is presented with proper units and significant figures, and conclusions are supported by evidence from the simulations.
Perform the following virtual experiments using the interactive simulation tools below.
Visualize an elliptical satellite orbit and verify Kepler's Laws. Observe velocity changes and equal area sweeping.
Calculate complete orbital parameters for any satellite orbit. Enter altitude and eccentricity to compute all key values.
Compare GEO, MEO, LEO, and HEO orbits side-by-side. Visualize relative sizes, periods, and ground tracks.
| Parameter | LEO | MEO | GEO | HEO |
|---|---|---|---|---|
| Altitude | 400 km | 20,200 km | 35,786 km | 500 × 40,000 km |
| Period | 1.5 hrs | 12 hrs | 23.9 hrs | 12 hrs |
| Velocity | 7.67 km/s | 3.87 km/s | 3.07 km/s | 1.5 – 10 km/s |
| Latency (RTT) | ~2.7 ms | ~135 ms | ~239 ms | Variable |
| Ground Track | Moving fast | Figure-8 | Stationary | Long dwell at apogee |
Determine when a satellite is visible from a ground station and visualize its ground track over Earth.
Calculate satellite coverage area based on altitude and minimum elevation angle. Determine constellation size for global coverage.
Follow these guidelines to prepare a comprehensive and well-structured laboratory report.
| Component | Weight | Criteria |
|---|---|---|
| Theory & Background | 15% | Completeness, accuracy, proper referencing |
| Procedure Description | 10% | Clarity, completeness, reproducibility |
| Data Presentation | 20% | Tables, graphs, units, significant figures |
| Results & Analysis | 30% | Correct calculations, physical insight, error analysis |
| Discussion & Conclusions | 15% | Critical thinking, connections to real systems |
| Report Quality | 10% | Organization, grammar, formatting, professionalism |